Big Idea: Negative numbers help us model many real-world situations.
Essential Question: How can I study multiplication patterns with integers?
Problem 4.2:
5x5= 25
5x4=20
5x3=15
5x2=10
5x1=5
5x0=0 A.Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller. As the integers got smaller, the product decreased by 5 each time. For example, 5x5=25, 5x4=20. 20 is 5 less than 25. B.1. Use the patterns you observed to predict 5 x-1. Explain your reasoning. 5x-1= -5. Since the integer decreased by 1 (-1 is 1 less than 0), the answer will decrease by 5. Since 5x0=0, 5 must be taken from 0 to get -5. 2. Write the next 4 equations in the pattern. 5 x-2=-10, 5 x-3= -15, 5 x-4=-20, 5 x-5=-25 C. Complete the equations below and use them to help you answer parts D&E.
5 x-4=? 4 x-4=? 3 x-4=? 2 x-4=? 1 x-4=? 0 x-4=?
-20 -16 -12 -8 -4 0 D. Describe any patterns you observe in the way the products change as the integers multiplied by -4 get smaller. The products all decrease by 4 as the integer decreases by 1. For example: 5 x-4= -20, and 4 x-4=-16. -16 is 4 less than -20. E. 1. Use the patterns you observed to predict -1 x-4. Explain your reasoning -1 x-4= 4. A negative multiplied by a negative makes a positive. Since -1 and -4 are both negative, their product will be positive. 2.Write the next 4 equations in the pattern. -1 x-5=5, -1 x-6=6, -1 x-7=7, -1 x-8=8 F. Find the following products: 1. -3 x7 2. 5 x-8 3. -11 x -12 4. -3.6 x 2.7 -21 -40 -132 -9.72
Problem 4.2 Follow-up: 1a. Find -6x7 and 7x-6 -6x7= -42 7x-6= -42 1b. When you multiply integers, does the order of the number matter? No, it does not. Multiplication has the commutative property, which means that the numbers can be switched around, and the answer will not change. 2a.Find -6+7 and 7+-6 -6+7= 1 7+-6= 1. 2b. When you add integers, does the order of the numbers matter? No, it does not. Addition also has the commutative property. The numbers can be in any order and the answer will remain the same. 3a. Find -6- 7 and 7- -6. -6-7= -13 7- -6= 13 3b. When you subtract integers, does the order of the numbers matter?
The order matters because if the numbers are switched, you are taking different quantities from different numbers. For example, 3-1. You are taking 3 from 1. But, if you switch it to 1-3, it is a completely different problem. You are now taking 3 from 1. The order of the numbers matters in subtracting integers. 4. When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain. No, it is not true. A negative multiplied by a negative is a positive.
4/25/10
Big Idea: Negative numbers help us model many real-world situations.
Essential Question: How can I study multiplication patterns with integers?
Problem 4.2:
5x5= 25
5x4=20
5x3=15
5x2=10
5x1=5
5x0=0
A. Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller. As the integers got smaller, the product decreased by 5 each time. For example, 5x5=25, 5x4=20. 20 is 5 less than 25.
B. 1. Use the patterns you observed to predict 5 x-1. Explain your reasoning. 5x-1= -5. Since the integer decreased by 1 (-1 is 1 less than 0), the answer will decrease by 5. Since 5x0=0, 5 must be taken from 0 to get -5.
2. Write the next 4 equations in the pattern. 5 x-2=-10, 5 x-3= -15, 5 x-4=-20, 5 x-5=-25
C. Complete the equations below and use them to help you answer parts D&E.
5 x-4=? 4 x-4=? 3 x-4=? 2 x-4=? 1 x-4=? 0 x-4=?
-20 -16 -12 -8 -4 0
D. Describe any patterns you observe in the way the products change as the integers multiplied by -4 get smaller. The products all decrease by 4 as the integer decreases by 1. For example: 5 x-4= -20, and 4 x-4=-16. -16 is 4 less than -20.
E. 1. Use the patterns you observed to predict -1 x-4. Explain your reasoning -1 x-4= 4. A negative multiplied by a negative makes a positive. Since -1 and -4 are both negative, their product will be positive.
2. Write the next 4 equations in the pattern. -1 x-5=5, -1 x-6=6, -1 x-7=7, -1 x-8=8
F. Find the following products:
1. -3 x7 2. 5 x-8 3. -11 x -12 4. -3.6 x 2.7 -21 -40 -132 -9.72
Problem 4.2 Follow-up:
1a. Find -6x7 and 7x-6 -6x7= -42 7x-6= -42
1b. When you multiply integers, does the order of the number matter? No, it does not. Multiplication has the commutative property, which means that the numbers can be switched around, and the answer will not change.
2a. Find -6+7 and 7+-6 -6+7= 1 7+-6= 1.
2b. When you add integers, does the order of the numbers matter? No, it does not. Addition also has the commutative property. The numbers can be in any order and the answer will remain the same.
3a. Find -6- 7 and 7- -6. -6-7= -13 7- -6= 13
3b. When you subtract integers, does the order of the numbers matter?
The order matters because if the numbers are switched, you are taking different quantities from different numbers. For example, 3-1. You are taking 3 from 1. But, if you switch it to 1-3, it is a completely different problem. You are now taking 3 from 1. The order of the numbers matters in subtracting integers.
4. When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain. No, it is not true. A negative multiplied by a negative is a positive.